When you don't even have to walk to the bar, what more can you want? Yet Stephanie Debere yearned for a fantasy adventure ...

Arrive at Cap Juluca, on Anguilla's north-western shore, and you are soon aware that you have entered a cocoon, fire-walled against stress and urgency. The hotel's drive is flanked by salty inlets and when you pass through the reception and scan the long crescent of sand on the other side, with a strung-out row of white Moorish-style villas rising from jungle-green vegetation, it feels as if you have stepped through the changing room in the cult Seventies children's programme Mr Ben.

Golf buggies drop guests at the soothingly named villas (Jonquil, Sienna, Persimmon). Each contains six rooms of surgically cool elegance, with white tiled floors and stuccoed walls amplifying the sense of space. Heavy, slatted wooden shutters open on to a balcony where breakfast is served every day, overlooking the luminous aquamarine bay and St Martin's mountainous mossy-green folds six miles away. Most exciting is the glass-walled bathroom, with a tub wide enough for two and a private walled terrace.

Despite turrets and domes, the 18 ultra-bright villas embody visionary simplicity. Six are for private hire: citadels to the glitterati, with high-walled courtyards containing ceramic-tiled pools. A mere 16 miles by three, Anguilla has shunned mass tourism. Steeped in discretion and offering gratification taken to extremes, it is hardly surprising that Cap Juluca attracts the likes of Sharon Stone, Janet Jackson and Mel Gibson.

The long beach guarantees privacy. Can't face walking from your sunlounger to George's beach restaurant to order Mediterranean snacks? Then display the service flag on your umbrella and a steward will oblige. Don't want to leave the tranquillity of your room for the spa? No problem, your Jamu massage will come to you. Staff at Cap Juluca are not obsequious, but they take pride in doing things perfectly.

After a couple of days' relaxation, managing little bar transferring ourselves between restaurants, tennis courts and the sea, it felt like time to do something. But how could we enjoy a change of scene without breaking Cap Juluca's spell? Unsurprisingly, the hotel has the answer: the next morning we were submerged in jet-set fantasy as our private 38-foot speedboat lifted its gleaming white nose from the water and surged out of Maunday's Bay. Sarongs flapping, hair flying and grins pushed back to our ears by the wind, we stood up and held tight in order to save our spines as the boat bounced erratically off oncoming waves, spraying us with foam. So this was what it felt like to own a speedboat. This was what it's like to be James Bond.

Thirty minutes later, we pulled into a bay of innumerable blues on an uninhabited mile-square nugget just north of Anguilla. As we stepped ashore, our jet-set personas were swept aside by our tropical castaway selves. We scanned a beachscape with foamy waves breaking over coral just out to sea and sculptures of bleached driftwood protruding from sand that was like pearl dust. There was not a footprint in sight.

Perhaps the only thing missing were the palms. Instead, bulbous, viciously-spiked cacti have colonised Prickly Pear Island. Walking shores such as these, it is unnervingly easy to imagine what it would be like to be here alone, without resources or means of escape. In the 18th century, Britain and France fought for supremacy in these waters, assisted in battle by privateers, and Anguilla passed between the European powers. Shipwreck survivors or deserters could easily have washed up on a beach like this, I thought. Diving down on the inshore reef to examine the fish (ignoring the fact that I was aided by fins and mask), I was the castaway diving for survival – for clams or crayfish to eat.

It's astounding how quickly you can start believing that virtually all of the stress and much of the clutter in your life is unnecessary. We were taunted by images of a simpler way of living – yet we were quite happy to have our fantasies interrupted by a call for lunch from Elvis and Wayne, our Cap Juluca boat drivers and the personifications of Caribbean cool. They had unobtrusively barbecued a feast of delicious blackened steak, swordfish and chicken served with Epicurean salads. We ate on the verandah of an abandoned wooden hut overlooking the beach, little black and yellow birds called banana chats gathering around in search of nibbles.

We spent the afternoon reading and doing nothing, grappling with the concept of such remoteness. Then came re-immersion in the decadent fantasy as we boarded the boat and whizzed towards Anguilla's shore. At Little Bay, we swam beneath cliffs covered in aloes and cactus, dotted with the nests of comic, prehistoric-looking pelicans. Then we slid back into Maunday's Bay. After a day at Prickly Pear, it seemed as if we were returning to a hub of activity. We could swim, play croquet, sail, windsurf. or just take sorbet on the beach. But we soon settled back into the pace, feasting that night in the hotel's flagship restaurant, Pimm's, designed like a giant Berber tent on a coral outcrop.

The Facts

Getting there

Stephanie Debere travelled as a guest of Abercrombie & Kent (0845 0700613, www.abercrombiekent.co.uk). Seven nights at Cap Juluca cost from £1,755 per person (b&b), with BA and Liat flights.